Kevin O. McCarthy’s battle to become the next speaker of the House will not end until Oct. 29, when votes are counted on the House floor, but it will be won or lost in three crucial days this week.

After days of courting lawmakers in private conversations and small groups, the House majority leader kicked off a high-stakes campaign to assure conservatives and unify his party Tuesday night in the confines of the Capitol Hill Club’s Eisenhower Room. It will culminate Thursday in a closed-door vote of the House Republican Conference, where he will be pressed not only to win his party’s nomination for speaker — he is all but assured of winning the requisite majority — but to show sufficient dominance to quell a potential floor challenge three weeks later.

All depends on whether he can convince a few dozen of the House’s most conservative members that he will not simply continue the policies and practices of outgoing Speaker John A. Boehner, who has deeply frustrated the party’s right flank.

“McCarthy’s pitch was, I’m not John Boehner, I’m going to run things differently, I’m my own man,” said Rep. Blake Farenthold (R-Tex.) after leaving Tuesday night’s meeting of roughly 60 members. “And I think that is a case that he does have to make. One of the things I hear all the time from my constituents back in Texas is, we don’t want John Boehner 2.0.”

But interviews with lawmakers who attended the meeting indicated that those words will not be enough for many. The question is whether that number will extend much past 28 — the number that would likely block McCarthy from a majority on the House floor.

A few hard-core critics of the sitting GOP leadership said they were determined to push the race past Thursday’s party vote: “Personally I hope this will be resolved on the floor of the House, not in the conference,” said Rep. Walter Jones Jr. (R-N.C.), who is supporting Florida Rep. Daniel Webster for speaker. “I think the American people have a right to see and understand why we vote a certain way.”

Rep. Mark Meadows (R-N.C.), who moved to force Boehner out of office this summer and has not committed to a speaker candidate, said that at least 40 Republicans have yet to decide but said McCarthy made a “compelling case” to the members who gathered Tuesday. But he joined other members in suggesting the party cast aside its current rules and instead only nominate a speaker candidate if he or she is able to garner the 218 votes necessary to win the floor vote “so we work our differences in conference before we ever have go to the floor.”

McCarthy is faced with not only quelling conservative doubts but also addressing the uproar over comments he made on Fox News Channel last week suggesting that a Republican-appointed special committee on the 2012 Benghazi attacks was motivated by politics. Those comments have been criticized by Republicans across the ideological spectrum, who have raised questions about his ability to serve as an able and reliable spokesman for his party.

The comments emboldened an 11th-hour challenger, Rep. Jason Chaffetz (R-Utah), who says the party needs a “speaker who can speak.”

McCarthy addressed the criticism during a Wednesday news conference of House GOP leaders: “I could have said it in a different manner, yes. And I think at any given time, somebody could always say something better. Over time, we’ll prove that we have a very good message. I think the job of the speaker is to be a team captain, all part of a team. We’ve got a lot of members inside this conference that lead a very good job of getting the message out, and we will continue to do it.”

The speaker candidates will address a larger group of House conservatives Wednesday afternoon in the Capitol basement, and all Republican members are invited to a Thursday morning Q&A session scheduled just hours before the nomination meeting is set to begin.

Asked after the Tuesday night meeting whether Republicans would unite behind the party nominee, few members pledged outright to do so.

“I’ve always been someone in primaries where we duked it out in the primary and we got together in the general,” said Rep. Trent Franks (R-Ariz.). “That’s always been my perspective, but this has some unique twists to it, and I have to at least give whatever these discussions are room to manifest.”

Said Farenthold: “Whoever gets nominated by the conference has got to have the leadership skills to pull together 218 to be able to support him. If he can’t get 218 for himself, it’s going to be a problem.”